Fractional-order Memristive Neural Networks Research Articles

Finite-Time Adaptive Synchronization and Fixed-Time Synchronization of Fractional-Order Memristive Cellular Neural Networks with Time-Varying Delays

Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems.

Adaptive finite-time passivity and synchronization of coupled fractional-order memristive neural networks with multi-state couplings

In this article, the adaptive finite-time passivity (FTP) and finite-time synchronization (FTS) of coupled fractional-order memristive neural networks with multi-state couplings (CFMNNMCs) are investigated. Firstly, a sufficient condition for guaranteeing the FTP of CFMNNMCs is obtained by developing an edge-based adaptive strategy and a state-feedback controller. Furthermore, a node-based adaptive controller is designed to ensure the FTP of CFMNNMCs. Additionally, with the help of properties of Gamma function and some inequality techniques, the adaptive FTS problem for the considered network model is addressed. Finally, two numerical examples are given to demonstrate the validity of the adaptive FTP and FTS criteria.

Adaptive Output Synchronization of Coupled Fractional-Order Memristive Reaction-Diffusion Neural Networks

This article discusses the adaptive output synchronization problem of coupled fractional-order memristive reaction-diffusion neural networks (CFOMRDNNs) with multiple output couplings or multiple output derivative couplings. Firstly, by using Lyapunov functional and inequality techniques, an adaptive output synchronization criterion for CFOMRDNNs with multiple output couplings is proposed. Then, an adaptive controller is designed for ensuring the output synchronization of CFOMRDNNs with multiple output derivative couplings. Finally, two numerical examples are given to verify the effectiveness of the theoretical results.

Mittag–Leffler stability and stabilization of delayed fractional-order memristive neural networks based on a new Razumikhin-type theorem

The Mittag–Leffler stability and stabilization of delayed fractional-order memristive neural networks(DFMNNs) are investigated in this paper. First, two new fractional Halanay inequalities are established by solving two fractional-order non-autonomous differential inequalities. Next, by using the proposed fractional Halanay inequalities, a novel Razumikhin-type theorem for Mittag–Leffler stability of delayed fractional-order systems is presented, which is an extension of the so-called Razumikhin theorem for integer-order delayed differential systems. Applying the Razumikhin-type theorem to the DFMNNs, several Mittag–Leffler stability and stabilization criteria are obtained. Finally, the validity of the proposed results is shown by two numerical examples.

Quasi-projective and finite-time synchronization of fractional-order memristive complex-valued delay neural networks via hybrid control

<abstract><p>We focused on the quasi-projective synchronization (QPS) and finite-time synchronization (FNTS) for a class of fractional-order memristive complex-valued delay neural networks (FOMCVDNNs). Rather than decomposing the complex-valued system into its real and imaginary components, we adopted a more streamlined approach by introducing a lemma associated with the complex-valued sign function. This innovative technique enabled us to design a simpler discontinuous controller. Then, based on the finite-time Lemma, measurable selection theorem, Lyapunov function theory, properties of the Mittag-Leffler function, and the fractional-order Razumikhin theorem, various substantial results were derived using a novel hybrid control scheme. In conclusion, we presented numerical simulations to illustrate the practical effectiveness of our theoretical findings.</p></abstract>

Novel results on asymptotic stability and synchronization of fractional-order memristive neural networks with time delays: The [formula omitted] case

This paper investigates the asymptotic stability and synchronization of fractional-order (FO) memristive neural networks with time delays. Based on the FO comparison principle and inverse Laplace transform method, the novel sufficient conditions for the asymptotic stability of a FO nonlinear system are given. Then, based on the above conclusions, the sufficient conditions for the asymptotic stability and synchronization of FO memristive neural networks with time delays are investigated. The results in this paper have a wider coverage of situations and are more practical than the previous related results. Finally, the validity of the results is checked by two examples.

Quasi-synchronization and stabilization of discrete-time fractional-order memristive neural networks with time delays

In this article, the quasi-synchronization (Q-S) and stabilization of a sort of discrete-time fractional-order memristive neural networks (DFMNNs) with time delays are considered. First of all, the definitions of ħ-discrete fractional operator are given, some basic properties of difference operators are gained, and then according to the above definitions and properties, several flesh inequalities of discrete-time fractional-order difference are established, which greatly expands the existing results. In addition, by use of Lypunov direct method and some related lemmas obtained above, the adequate Q-S criteria are obtained for DFMNNs with time delays under the delay feedback controller. At the same time, we also yield the relevant conditions of stabilization. Finally, the validity and availability of the above theoretical results are verified by numerical simulations.

Predefined-time synchronization of fractional-order memristive competitive neural networks with time-varying delays

This article focuses on the predefined-time synchronization (PTS) of fractional-order memristive competitive neural networks (FMCNNs) with time-varying delays. According to the two-layer structural characteristics of CNNs, two kinds of distinctive discontinuous bilayer predefined-time control schemes with the fractional integrals are proposed: one is the double controllers based on piecewise Lyapunov function and the other is a controller with Lyapunov function and exponential function. Using the predefined-time stability theorems and applying fractional-order differential inequalities and other inequality techniques, some effective criteria are obtained to assure the PTS of two FMCNNs in terms of algebraic inequalities, which are very succinct and avert complicated calculations. Besides, the predefined time (PT) is set to an arbitrary positive parameter in these controllers and is entirely irrelevant to the initial values. Finally, two concrete examples are given to verify the theoretical results.

Stabilization of reaction–diffusion fractional-order memristive neural networks

This paper investigates the stabilization control of fractional-order memristive neural networks with reaction–diffusion terms. With regard to the reaction–diffusion model, a novel processing method based on Hardy–Poincarè inequality is introduced, as a result, the diffusion terms are estimated associated with the information of the reaction–diffusion coefficients and the regional feature, which may be beneficial to obtain conditions with less conservatism. Then, based on Kakutani’s fixed point theorem of set-valued maps, new testable algebraic conclusion for ensuring the existence of the system’s equilibrium point is obtained. Subsequently, by means of Lyapunov stability theory, it is concluded that the resulting stabilization error system is global asymptotic/Mittag-Leffler stable with a prescribed controller. Finally, an illustrative example about is provided to show the effectiveness of the established results.

Finite-time synchronization of fractional-order delayed memristive fuzzy neural networks

This paper deals with the finite-time synchronization (FTS) for a class of fractional-order memristive fuzzy neural networks (FOMFNNs) with leakage and transmission delays. Two types of discontinuous control schemes with leakage and transmission delays are designed: one is the state feedback control and the other is the fractional-order adaptive control. Based on differential inclusion theory and fractional-order differential inequalities, several new delay-independent algebraic conditions are derived to guarantee the FTS of drive-response FOMFNNs with leakage and transmission delays. Moreover, the estimation of the upper bound of the settling time for the FTS is given as well. Ultimately, two numerical examples with simulations are furnished to demonstrate the feasibility and availability of the theoretical results.

Passivity and passification of fractional-order memristive neural networks with time delays

A class of fractional-order memristive neural networks (FMNNs) with time delays is studied. At first, the original network system is converted to fractional-order uncertain one to simplify the analysis by a variable transformation. Successively, some new LMIs-based passivity criteria are derived by differential inclusions, set-valued maps, inequality techniques and linear matrix inequality approach. Furthermore, a feedback control protocol is designed to solve the passification problem for the considered system, whose feedback control effect on different neurons can be changed artificially, which can be better applied to neural networks. The obtained results include some existing ones as special cases. A numerical example is proposed to illustrate the theoretical results.

Switching-Jumps-Dependent Quasi-Synchronization Criteria for Fractional-Order Memrisive Neural Networks

This paper investigates the switching-jumps-dependent quasi-synchronization issue for fractional-order memristive neural networks (FMNNs). First, a simplied linear feedback controller is applied. Then, in terms of several fractional order differential inequalities and two kinds of Lyapunov functions, two quasi-synchronization criteria expressed by linear matrix inequality (LMI)-based form and algebraic form are established, respectively. Meanwhile, the co-designed scheme for error bound and control gain is established. Compared with the previous quasi-synchronization results, a strong assumption that the system states must be bounded is removed. Finally, some simulation examples are carried out to display the feasibility and validity of the proposed analysis methods.

Delay-dependent and order-dependent conditions for stability and stabilization of fractional-order memristive neural networks with time-varying delays

The stability and stabilization problems of fractional-order memristive neural networks with time-varying delays are addressed. Based on Jensen-based integral inequalities, novel delay-dependent and order-dependent stability conditions for fractional-order memristive neural networks with time-varying delays are established. The proposed stability criterion is in terms of linear matrix inequalities and is easy to be verified and applied. Then, a linear feedback control law that stabilizes fractional-order memristive neural networks with time-varying delays is designed by utilizing the obtained stability conditions. Two numerical examples are used to illustrate the effectiveness and less conservativeness of the proposed results.

Quantized control for finite-time synchronization of delayed fractional-order memristive neural networks: The Gronwall inequality approach

This paper is concerned with the finite-time synchronization (FTS) of delayed fractional-order memristive neural networks (FMNNs) by using quantized control. Firstly, two kinds of quantized controllers are designed to eliminate the residual synchronization errors that appear owing to the characteristics of memristive connection weights. Then, to derive α-dependent FTS criteria for drive–response FMNNs, the Gronwall inequality technique is used by combination with the direct estimation method. Compared with the existing results, the advantages of the derived synchronization criteria are discussed from the aspects of both theory and simulation. In addition, the relationships between the finite-time parameter and the quantization parameters are displayed. It reveals that there is a compromise between the admissible finite-time and the saved network bandwidth. Finally, two examples are given to illustrate the effectiveness of the obtained results.

Novel controller design for finite-time synchronization of fractional-order memristive neural networks

In this paper, it will concentrate on the controller designs for finite-time synchronization(FTS) of fractional-order memristive neural networks(FMNN). According to the features of neural networks, different class of controllers are formed to achieve the finite-time synchronization. Moreover, based on Lyapunov technique and fractional calculus theory, finite-time synchronization conditions have been established, and corresponding upper bound of settling time are presented. At last, a few numerical examples are introduced to illustrate the effectiveness and feasibility of the control algorithms and resulted conclusions.

Finite-Time Synchronization of Uncertain Fractional-Order Delayed Memristive Neural Networks via Adaptive Sliding Mode Control and Its Application

Finite-time synchronization (FTS) of uncertain fractional-order memristive neural networks (FMNNs) with leakage and discrete delays is studied in this paper, in which the impacts of uncertain parameters as well as external disturbances are considered. First, the fractional-order adaptive terminal sliding mode control scheme (FATSMC) is designed, which can effectively estimate the upper bounds of unknown external disturbances. Second, the FTS of the master–slave FMNNs is realized and the corresponding synchronization criteria and the explicit expression of the settling time (ST) are obtained. Finally, a numerical example and a secure communication application are provided to demonstrate the validity of the obtained results.

Finite-time synchronization of fractional-order memristive neural networks via feedback and periodically intermittent control

This paper discusses the finite-time synchronization (FTS) of fractional-order memristive neural networks (FMNNs) with time-varying delays. Firstly, based on Gronwall–Bellman inequality and the fractional-order derivative of the power function, two novel propositions on finite-time fractional functional differential inequality are built. Secondly, the feedback controller and intermittent controller designed in this paper are all delay-independent controllers, which can work even when the prior state cannot be measured or the specific time delay function is unknown. Thirdly, in addition to the traditional Lyapunov function with absolute value form, a more general and flexile Lyapunov function based on p-norm form is constructed to analyze the criteria of FTS. Meanwhile, an improved estimation of settling time of fractional system is given explicitly, which is more accurate and general than the existing results. Eventually, the validity of theoretical analysis is confirmed by numerical examples.

Finite-time reliable sampled-data control for fractional-order memristive neural networks with quantisation

ABSTRACT This paper addresses the reliable finite-time stabilisation problem for a class of fractional-order memristor neural networks under sampled-data controller influenced by the quantisation signal and actuator failures. Precisely, the framework of observer has been initiated for estimating unmeasured state and remunerate the actuator faults with nonlinearities in the controller. Precisely, quantiser is incorporated in the network can reduce the process of transmitting data. Subsequently, activation function approach bringing together with traditional indirect Lyapunov theory endows some sufficient conditions in the frame of linear matrix inequalities to assure the finite-time stabilisation criterion for the addressed neural networks under the proposed reliable sampled-data control. Explicitly, the state feedback control and observer gain matrices are attained by solving the developed linear matrix inequalities. Convincingly, two numerical simulations are explored to substantiate the excellence and potentiality of the developed control law.

Synchronization of fractional-order memristive recurrent neural networks via aperiodically intermittent control.

In this paper, synchronization of fractional-order memristive recurrent neural networks via aperiodically intermittent control is investigated. Considering the special properties of memristor neural network, differential inclusion theory is introduced. Similar to the aperiodically strategy of integer order, aperiodically intermittent control strategy of fractional order is proposed. Under the framework of Fillipov's solution, based on the intermittent strategy of fractional order systems and the properties Mittag-Leffler, sufficient criteria of aperiodically intermittent strategy are obtained by constructing appropriate Lyapunov functional. Some comparisons are given to demonstrate the advantages of aperiodically strategy. A simulation example is given to illustrate the derived conclusions.

Quasi-Synchronization of Nonidentical Fractional-Order Memristive Neural Networks via Impulsive Control

This paper investigates the quasi-synchronization of nonidentical fractional-order memristive neural networks (FMNNs) via impulsive control. Based on a newly provided fractional-order impulsive systems comparison lemma, the average impulsive interval definition, and the Laplace transform, some quasi-synchronization conditions are obtained with fractional order 0 < α < 1 . In addition, the error convergence rates and error boundary are also obtained. Finally, one simulation example is presented to show the validity of our results.